Representation Failure∗

Matias IaryczowerPrinceton

Galileu KimPrinceton

Sergio MonteroRochester†

September 16, 2019

Abstract

We use rich data on thousands of candidates in three Brazilian leg-islative elections to (i) quantify the relative value voters place on can-didates’ policy positions and valence attributes, (ii) evaluate voters’welfare given the set of candidates they face, and (iii) explain whenand why candidates choose policy positions that diverge from voters’preferences. We find that the “supply side” of politics imposes largewelfare losses on Brazilian voters: in half of the country, average voterwelfare is at least 80% lower than an ideal benchmark. Through coun-terfactual experiments, we show that institutional reforms aimed atimproving the quality of representation may have sizable unintendedconsequences, due to equilibrium policy adjustments.

Keywords: elections, ideology, candidate valence, voter welfare.Word Count: 11,247

∗We thank seminar audiences at Princeton, Rochester, University of Houston, and theEuropean Political Science Association Annual Meeting for comments.†Matias Iaryczower: Department of Politics, Princeton University, email: mi-

aryc@princeton.edu; Galileu Kim: Department of Politics, Princeton University, email:galileuk@princeton.edu; Sergio Montero: Departments of Political Science and Economics,University of Rochester, email: smontero@rochester.edu.

1 Introduction

In recent years, voters in the U.S., Brazil, Argentina, Spain, and other democ-

racies around the world, have expressed discontent with the entire political

system. From large public demonstrations to overwhelming disapproval in

opinion polls, large fractions of voters seem dissatisfied with all the alterna-

tives available to them. Such a systemic representation failure could severely

undermine democracy. Shortages of palatable candidates can limit citizens’

ability to elect public officials who can implement their preferred policies, or

whom voters view as well qualified to be in office. More broadly, this can lead

to general disenchantment of citizens with democratic institutions, paving the

way for authoritarian attempts.

Democracy is, of course, bound to be imperfect. First, the set of individuals

who decide to dedicate their lives to politics and public service is limited.

Many talented or qualified individuals choose to remain in the private sector.

Moreover, the political system may push away individuals who might otherwise

consider a career in politics due to their gender or socioeconomic background.

Second, the candidates that do run for office might not have incentives to put

forth policies that represent their constituencies’ best interests. The extent to

which each of these factors impacts voters’ welfare depends fundamentally on

how much voters value them. Assessing representation failures in any given

democracy, therefore, requires estimating voters’ preferences over candidates’

potential attributes.

In this paper, we take on this problem in the context of elections for the lower

1

house of Brazil’s National Congress (Camara dos Deputados). We use rich

data on thousands of candidates in three recent elections to (i) quantify the

relative value that voters give to policy and valence, and (ii) evaluate the

welfare loss to voters brought by the characteristics and policy choices of the

set of candidates they face. We then (iii) estimate a model of the “supply

side” of politics to explain when and why candidates choose policy positions

that diverge from voters’ preferences.

Brazil’s electoral system makes the country a natural focal point for this analy-

sis. First, in Brazil’s open-list proportional-representation (PR) system, voters

cast their ballots overwhelmingly for individual candidates rather than parties.

This allows us to link voters’ decisions with individual candidates’ character-

istics rather than the characteristics of an entire list, as would be the case in

a closed-list PR system like that of Argentina. Second, voters can typically

choose from among a large number of candidates in each state, ranging from 46

in the state of Tocatins to more than 1,200 in Sao Paulo (2014 election). This

richness of choice gives us great purchasing power to map candidates’ charac-

teristics to voters’ preferences. Third, differently from majoritarian elections,

this variant of PR elections minimizes incentives to vote strategically, removing

another obstacle to estimating voters’ preferences.

To carry out this exercise, we gather data on the 15,698 candidates running

for a seat in the Camara dos Deputados in the 2006, 2010, and 2014 elections,

across all 27 legislative districts (26 states and the Distrito Federal). For each

candidate running for office, we observe the number of votes obtained by the

2

candidate in each municipality, along with a rich set of individual character-

istics, including their previous professional experience, political experience,

education, and gender. For over 10,000 candidates, we are also able to obtain

a measure of their policy positions using individual campaign contributions,

following the methodology outlined in Bonica (2014).

To estimate voters’ preferences, we use the random-coefficients logit model of

Berry, Levinsohn, and Pakes (1995) (BLP). This approach relaxes the inde-

pendence of irrelevant alternatives assumption of standard multinomial logit

models, and enables us to estimate flexible but computationally feasible substi-

tution patterns across candidates, which is essential for our analysis. Further-

more, it allows us to explicitly account for unobserved candidate heterogeneity

in valence attributes (e.g., charisma).

Our preference estimates separately quantify the value voters place on can-

didates’ policy positions and valence characteristics. With this information,

we evaluate voters’ welfare given the actual set of candidates they face in the

data. We then compare this measure with an ideal (but attainable) bench-

mark, computed as the welfare derived from a hypothetical candidate with

highest in-sample valence who adopts the voter’s optimal policy. The results

uncover a considerable failure of the Brazilian political system: across Brazil’s

5,507 municipalities, we estimate an average welfare loss of 77% relative to the

ideal benchmark.

Our estimates reveal that, in many districts, a significant fraction of the welfare

loss is due to ideological incongruence between voters and politicians. To

3

understand why politicians’ policy choices diverge from the preferences of their

constituents, we estimate a model of the “supply side” of politics, in which

candidates’ policy positions emerge explicitly as equilibrium choices.

The estimates provide two important lessons. First, we find that candidates

with valence advantages are able to put forth policies that are more in line with

their own preferences, to the detriment of party interests and voter welfare.

Second, we show that variation in candidates’ power vis-a-vis parties explains

a significant fraction of the welfare loss to voters that is due to ideological

mismatch with politicians. In particular, districts in which parties are weak

relative to their candidates tend to experience larger policy welfare losses.

As this discussion illustrates, candidate valence affects voters’ welfare both

directly and through its influence on policy choices. Thus, reforms aimed at

improving the quality of representation (e.g., increasing candidates’ educa-

tion) could have unintended consequences leading to lower, or even negative,

welfare changes. To evaluate this possibility, we simulate the effect of a posi-

tive shift in the distribution of candidates’ valence. We show that, while the

valence shock has an overwhelmingly positive direct effect on welfare, the in-

direct effect due to candidates’ equilibrium policy adjustments reduces these

gains on average, and leads to welfare losses for some voters. We further illus-

trate the importance of indirect equilibrium effects in a second counterfactual

experiment where we restrict electoral competition to the largest parties.

4

2 Related Literature

The early literature on legislative bodies in Latin America focused on legisla-

tive autonomy under strong presidentialism (Linz 1990, Carey and Shugart

1995, O’Donnell 1998). As the threat of authoritarian reversals diminished,

scholarly focus shifted to understanding how formal and informal institu-

tions shape legislative behavior and legislative careers. These papers pro-

vided the basic characterization of the Brazilian political system we now

have: (i) parties are weak, under-resourced, and often unable to constrain

individual opportunistic behavior by individual legislators (Mainwaring 1999,

Samuels 2003, Desposato 2006, Klasnja and Titiunik 2017), (ii) open-list pro-

portional representation, and the lack of formal mechanisms channeling re-

sources to congressional party leaders, promote candidate-centric legislative

careers (Mainwaring, Scully, et al. 1995, Samuels 2003), and (iii) presidents

have systematically used pork and cabinet positions to “buy” legislative sup-

port, leading to what is known as presidential coalitionism (Neto and da Matriz

1998, Neto 2006).

In part due to presidential coalitionism, the most common approaches to esti-

mating legislators’ preferences in the U.S., which rely on the assumption that

legislators vote “sincerely,” have been regarded as unreliable in the Brazil-

ian context. To overcome this problem, Zucco (2009), Zucco and Lauderdale

(2011), and Power and Zucco (2012) estimate legislators’ ideal points using

surveys (see Power (2010)), and use these estimates to ascertain the influence

of external factors on legislators’ voting behavior.

5

Research on voters’ preferences, and how these connect with electoral choices,

is more sparse.1 Power and Rodrigues-Silveira (2019) leverage the legislative

survey data to obtain a measure of voters’ ideology at the municipality level.

Specifically, they measure voters’ ideology in a given municipality as a weighted

average of the average ideological score of each party, with weights equal to

the vote share of each party in the municipality. One issue with this approach

is that the interpretation of this measure as reflecting voters’ ideology assumes

that voters’ decisions are driven only by ideological considerations. Thus, any

variation in candidates’ valence attributes that translates to votes (incum-

bency, gender, experience, etc.) is incorrectly construed as ideology. Instead,

our approach allows us to disentangle voters’ ideological preferences from their

tastes for valence attributes. Moreover, in doing so, we exploit variation in

policy choices and valence at the candidate level (elected and non-elected).

Our estimation strategy builds on the random-coefficients logit model of Berry,

Levinsohn, and Pakes (1995). This approach has been used extensively in eco-

nomics to estimate demand for differentiated products but has received little

attention in political science. We are aware of four papers that use the BLP

approach in electoral contexts. Rekkas (2007) and Gordon and Hartmann

(2013) use it to estimate the effect of campaign spending on electoral outcomes

in Canadian (legislative) and U.S. (presidential) elections, respectively. Mon-

tero (2016) estimates the effect of coalition formation on electoral outcomes

when parties invest in campaign activities, using data from the 2012 Mexican

1Ferraz and Finan (2008) study the effect of information about corruption on the elec-toral performance of majors. Klasnja and Titiunik (2017) estimate the electoral effect ofincumbency, also at the municipal level.

6

Chamber of Deputies election. Finally, Ujhelyi, Chatterjee, and Szabo (2018)

use the BLP approach to study protest votes in India. To our knowledge, our

paper is the first to use this approach to recover voters’ preferences for policy

relative to valence, in any electoral context.

3 Data

3.1 Context

We focus on elections of representatives to the lower house of the Brazilian

National Congress. The Camara dos Deputados is composed of 513 represen-

tatives, who are elected in 27 multi-member electoral districts, corresponding

to the country’s 26 states and the Distrito Federal of Brasilia. The magnitude

of each district is determined according to population, but no state may have

fewer than eight or more than seventy seats.2

Elections take place under an open-list proportional-representation (PR) sys-

tem. Each voter has one vote to cast, which can be given to a specific candidate

or (rare) to a party or coalition list. In each district, votes given to candidates

from each list are pooled and added to the votes received by the list to form a

total list vote. Seats are then distributed among lists proportionally to their

total list vote according to the D’Hondt method.3 Within each list, seats are

2The lower bound is binding for eleven states, and the upper bound is binding only forthe state of Sao Paulo. See Table A.1 in the Appendix.

3In each district, an electoral quotient is computed by dividing the total number of validvotes (i.e., excluding blank or void votes) by the number of available seats. Then eachtotal list vote is divided by the electoral quotient. The result of this division, disregarding

7

assigned to candidates in descending order of votes received. Representatives

are elected for four-year terms, with no constraints on reelection.4

The open-list PR system fosters a fragmented multiparty system (Mainwaring

1999). In the 2014 election, 28 parties placed candidates in the lower chamber.5

The dispersion of votes across multiple parties is partly the result of regional

vote concentration, but vote fragmentation occurs even at the local level. This

can be seen in the left panel of Figure A.4 in the Appendix, which plots the

empirical distribution of the effective number of parties for each district, using

vote shares at the municipal level.

Brazil has large socioeconomic disparities, which make for 27 highly hetero-

geneous electoral districts. This is illustrated in Figure A.1 in the Appendix,

where we plot the rural population share, median wage, and literacy rate at

the municipality level. Broadly, the most striking differences are between the

richer, more educated, and generally more urban south and southeast regions,

and the poorer, more heavily (subsistence) agricultural, and less dense north

and northeast regions. These disparities help explain some of the regional

variation in electoral performance across parties. Poorer municipalities tend

to vote overwhelmingly for the PT, which has pursued a progressive agenda

that has favored poor constituencies (Samuels 2004, Bohn 2011). On the other

hand, wealthier municipalities tend to favor the right-leaning PSDB (see Fig-

fractions, is the list quotient, which determines the number of deputies elected by the list.If there remain unallocated seats after the application of list quotients, these are distributedaccording to the highest averages method using the D’Hondt formula.

4Reelection rates are high for federal deputies, with over 74% of incumbents securingreelection in 2014.

5See Table A.2 in the Appendix for a list of all parties gaining seats in the Camara dosDeputados in 2014, with their respective vote and seat shares.

8

ures A.2 and A.3 in the Appendix).

3.2 Legislative Candidates

Differently from closed-list PR systems, Brazil’s electoral system puts individ-

ual candidates at the center of political choice. Indeed, the literature notes

that Brazilian elections tend to be candidate-centric rather than party-centric,

with voters effectively responding to candidate characteristics above party la-

bels (Mainwaring, Scully, et al. 1995, Mainwaring 1999, Samuels 2003, Klasnja

and Titiunik 2017). Understanding the drivers of voters’ choices, therefore, re-

quires that we analyze them at the candidate level.

To that end, we bring together data on all candidates running for a seat in

the Camara dos Deputados in the 2006, 2010, and 2014 elections. In total,

across these three elections and all 27 legislative districts, there were 15,698

candidates: 4,944 in 2006, 4,887 in 2010, and 5,867 in 2014. For each candidate

running for office, we observe the number of votes obtained by the candidate in

each municipality, along with a rich set of individual characteristics including

their previous professional experience, political experience, level of education,

and gender.6 For over 10,000 candidates, we are also able to obtain a measure

of their policy positions using individual campaign contributions, following the

methodology outlined in Bonica (2014). We describe this in detail below.

6This information can be obtained from the Brazilian electoral authority, the TribunalSuperior Eleitoral (TSE).

9

elected non-elected

0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00

white_collar

politician

incumbent

higher_edu

government

female

business

value

Proportion of individual characteristics across elected and non-elected candidates

Figure 1: Candidates Observable Non-Policy (Valence) Characteristics.

Figure 1 provides summary statistics of candidates’ observable non-policy char-

acteristics (following standard practice, we refer to these non-policy attributes

as valence). Overall, given the large number of candidates competing for seats,

there is a low proportion of incumbents in the candidate pool. However, in-

cumbents are disproportionately represented among candidates who secure a

seat in the chamber. The same type of selection occurs along other attributes:

while only about half of the candidates have higher education, this figure in-

10

creases to about 75% for elected candidates; women compose only about a

quarter of total candidates, but an even far lower percentage of elected candi-

dates; candidates with business or government (bureaucratic) experience make

about 10% of the pool of candidates, and they represent a significantly lower

proportion of elected candidates. Figure 2 further highlights these differences

for incumbency, education, gender, and age in terms of candidates’ vote shares.

Incumbency Higher Education

Gender (female) Age

Figure 2: Candidate Vote Shares (among registered district voters) by ValenceAttribute.

While the education, professional experience, gender, and other valence at-

tributes of candidates seem clearly important to voters, the policy choices

11

candidates make can also be relevant. In particular, voters in the U.S. and

elsewhere have been shown to be responsive to the ideological position candi-

dates put forward.7 Whether this is also true in Brazil, and how much weight

voters put on ideology relative to valence, is an empirical question.

Measuring how voters’ preferences for candidates vary with the policies the

candidates embrace requires a measure of both elected and non-elected can-

didates’ policy positions. Unfortunately, this information is hard to come by.

Indeed, there are no currently available estimates of both incumbents’ and

challengers’ policy positions for Brazilian legislative elections.8 To address

this problem, we follow the approach of Bonica (2014) to produce our own

estimates of candidates’ policy choices, using micro-level data on campaign

contributions for 2004-2014. We also use this approach to estimate the policy

positions of candidates in mayoral elections, which prove useful in the estima-

tion of our main model, as discussed later.

The intuition for how campaign contributions can be used to estimate politi-

cians’ policy positions is similar in spirit to that behind DW-Nominate. The

key assumption is that the contributor’s marginal benefit of giving to a par-

ticular candidate is decreasing in the distance between the contributor’s ideal

policy and the candidate’s choice. This implies that contributors give (weakly)

7See, e.g, Canes-Wrone, Brady, and Cogan (2002), Ansolabehere and Jones (2010), andIaryczower, Moctezuma, and Meirowitz (2018).

8Zucco (2009), Zucco and Lauderdale (2011) and Power and Zucco (2012) estimate legis-lators’ ideal points using surveys that ask them to place themselves and all the main politicalparties represented in the legislature on a left-right 10-point scale (see Power (2010)). Asthese papers suggest, estimation of incumbents’ ideal points via DW-Nominate or Ideal isproblematic due to widespread “vote-buying” of legislators through pork-barrel spendingand cabinet allocations.

12

more money to candidates that are closer to their ideal point, which in turn

allows us to rank candidates’ positions in the policy space. Bonica inter-

prets these estimates as politicians’ policy preferences. We only make the

assumption that these are the candidates’ policy choices, which could or not

correspond with their true preferences.9

To implement this approach, we use data on micro-level dyadic contributions,

including both individual and corporate donations.10 Since corporations may

donate to candidates strategically, we exclude them from our data and focus

on private contributions by non-partisans and non-politicians. In total, we

leverage over 650 thousand unique contributions at the federal level, and 3.8

million unique contributions at the local level.11 Because many non-viable

candidates tend to receive a small number of contributions, we are forced to

drop a sizable number of candidates from the database. Nevertheless, our final

sample includes 10,752 candidates across the three elections.12

We perform a battery of sanity checks of the external and internal validity

of our candidate policy estimates. The left panel of figure A.6 shows that

9Estimation is carried out by a modified correspondence analysis with a two-way fre-quency matrix, where rows correspond to unique contributors and columns to candidates.Each element in the matrix is the total amount of contributions made by contributor i tocandidate j, for the time span of our data. We then perform a singular value decompositionto retrieve ideal points for contributors and recipients.

10The campaign contribution data is available since the 2002 election, when the TSEmandated the disclosure of electoral campaign contributions to candidates at all levels ofgovernment. Importantly, the dataset uniquely identifies both contributors and recipients.

11We estimate scores separately for local and federal candidates, pooling across electoralcycles.

12The candidates for whom we are able to recover policy positions make an overwhelmingfraction of all candidates seriously contending for a seat in the Camara dos Deputados (seeFigure A.5 in the Appendix). In fact, only 0.02 % of the candidates for whom we don’thave policy data were ultimately elected. Table A.3 in the Appendix summarizes coverageof the final dataset by state and electoral cycle.

13

there is a strong correlation between policy positions within the same party

at both the local and federal level, while the right panel shows that our policy

estimates are correlated with the ideology scores estimated by Zucco (2009)

(on average, at the party level). Figure A.7, on the other hand, shows that

our estimates capture the leftward ideological shift of voters and parties in the

2000s found in Latinobarometer surveys.13

In the next section, we use this information on candidates’ valence characteris-

tics and policy choices, along with voting outcomes at the individual candidate

level, to estimate voters’ preferences. The key for doing this, of course, is that

voters can in principle give their vote to any candidate in the district, but

choose to give it to one with some particular attributes. Another alternative

that is de facto available to voters is to abstain or to cast a void vote. This

“outside option” is thus effectively competing with all the candidates for votes.

As Figure 3 illustrates, this, in itself, is a formidable alternative. The 29% av-

erage abstention rate and 8.6% average blank vote rate in what is formally

a compulsory voting system provide suggestive evidence that voters are not

enthusiastic about the candidates they face.

4 Voter Preferences

As noted, one of our main goals is to estimate voters’ preferences over both

candidates’ policy choices and valence characteristics. To that end, we employ

a random-coefficients logit model (BLP). The model treats candidates as bun-

13See Zucco and Lauderdale (2011).

14

Figure 3: Distribution of Abstention and Blank Vote Shares (among registeredvoters) in Each Municipality, by State.

dles of characteristics. In other words, voter i’s preference for candidate j can

be expressed as an aggregation of the value that the voter places on each of

the candidate’s attributes (e.g., education, experience, policy position). This

approach is well suited to our problem for four reasons.

First, as opposed to simply quantifying the relative value of voting for can-

didate j or j′, focusing on voters’ preferences for the underlying attributes of

each candidate allows us to gauge how voters trade off valence characteristics

for proximity in policy position. This, in turn, enables counterfactual analy-

ses of voter choice and welfare under alternative assumptions about potential

changes to the supply of candidates.

Second, the approach yields a substantial reduction in the dimensionality of

15

the problem. To appreciate this, note that, in our final sample, the 2014

election in the state of Sao Paulo alone features 870 candidates. Absent re-

strictions on preferences, attempting to capture how the policy choice of can-

didate j′ affects candidate j’s vote share would require 870× 870 (almost one

million) coefficients. The BLP formulation allows for rich heterogeneity in

preferences with a parsimonious specification by introducing random coeffi-

cients to a multinomial logit random utility framework. This delivers flexible,

but computationally feasible, substitution patterns across candidates that re-

lax the independence of irrelevant alternatives (IIA) assumption present in

standard multinomial logit models. This is particularly important in electoral

politics, as IIA would imply, e.g., that a left-wing candidate and a right-wing

candidate would benefit or lose equally (in percentage terms) from a change

in the policy position of another right-wing candidate.

Third, the model allows for unobserved heterogeneity in candidate valence.

This is key because, despite our access to detailed information about can-

didates, there remain electorally significant attributes, such as charisma or

trustworthiness, that cannot be measured reliably or exhaustively. The BLP

approach accounts explicitly for these unobservables as well as their influence

on candidates’ (endogenous) policy choices.

Finally, our problem and data are particularly well suited for this technique, as

we have rich variability in valence characteristics and policy positions from over

10,000 candidates across multiple constituencies and electoral cycles. This,

together with instrumental variables (IVs) described below, provides identifi-

16

cation and allows us to obtain precise estimates (Berry and Haile 2014).

4.1 Voter Preferences: Model

Voter i’s utility from selecting candidate j in state (district) n is given by

uijn = α1ipjn + α2ip2jn +X ′jnβ + ξjn + εijn, (4.1)

where Xjn is a vector of observable (exogenous) candidate characteristics,

pjn ∈ [−p, p] denotes candidate j’s (endogenous) policy position, and εijn

is an i.i.d. mean-zero Type-I Extreme Value (TIEV) random utility shock.14

The coefficients on the effect of the politician’s ideology are voter-specific, and

voter i’s ideal point or policy can be recovered as yi = −α1i/(2α2i).15 There

are other candidate characteristics not captured in Xjn that may affect voters’

preferences but are unobserved by the analyst (e.g., charisma). The term ξjn

explicitly accounts for this residual valence. While unobserved by the analyst,

ξjn is known to candidates, parties, and voters and is therefore potentially

correlated with j’s policy position, pjn.

We allow observed demographics to inform voters’ policy preferences. Specif-

ically, we assume that the coefficients (α1i, α2i) for voter i can be written as

αki = αk +D′n(i)γk + σkνki, (4.2)

14We describe how p > 0 is constructed in Footnote 20 below.15Voters with (rare) convex policy preferences, i.e., α2i ≥ 0, have ideal point yi = p

(yi = −p) if α1i ≥ 0 (α1i < 0).

17

where n(i) denotes the state in which voter i resides, Dn is a vector of demo-

graphic characteristics of state n, and (ν1i, ν2i)′ ∼ N(0, I2) are (unobserved)

i.i.d. idiosyncratic policy preference shocks. As we explain shortly, this rich

heterogeneity in preferences relaxes IIA and yields flexible substitution patters

across candidates. Note that, given this specification, the average voter utility

from selecting candidate j in state n is

δjn ≡2∑

k=1

(αk +D′nγk)pkjn +X ′jnβ + ξjn. (4.3)

4.2 Voter Preferences: Estimation

Our estimation methodology implements the BLP strategy using the Mathe-

matical Programming with Equilibrium Constraints (MPEC) approach of Su

and Judd (2012) for computational efficiency. Here, we summarize the main

ideas, emphasizing the intuition. For technical details, see Appendix B.

Consider first the simpler case where voters are homogeneous up to observed

covariates, which boils down to a standard multinomial logit random utility

model. Normalizing the average utility from abstaining or casting a void vote

to δ0n = 0, candidate j’s predicted vote share (among registered voters) can

be written in the familiar form (McFadden 1973)

sjn =exp(δjn)

1 +∑

j′∈Jn exp(δj′n), (4.4)

where Jn denotes the set of candidates running in state n. Taking logs of (4.4),

18

we can “invert” predicted vote shares to express them in terms of average voter

utilities: log(sjn)− log(s0n) = δjn. Then, replacing predicted vote shares with

their observed counterparts in the data, sjn, and using (4.3), we obtain

log(sjn)− log(s0n) =2∑

k=1

(αk +D′nγk)pkjn +X ′jnβ + ξjn, (4.5)

which is just a linear regression of the log-ratio of candidate j’s vote share

to the share of the “outside option” (abstaining or casting a void vote) on

endogenous (pjn) and exogenous covariates (Dn and Xjn).

Note that candidate j’s unobserved valence, ξjn, corresponds to the residual

of this regression. Thus, provided we have valid instruments Zjn for the en-

dogenous regressors, i.e., a vector of variables such that E[Zjnξjn] = 0, we

can estimate the parameters α, γ, and β from this linear regression via two-

stage least squares. Equation (4.5) makes transparent that the variation in

the data that identifies the parameters is variation in valence characteristics

and vote shares across candidates, together with variation in demographics

and the exogenous variation in policy choices captured by the instruments.

While the multinomial logit model is simple and computationally straightfor-

ward to estimate, it also imposes strong assumptions on voter preferences. In

particular, notice that log (sjn/sj′n) = δjn−δj′n. Thus, the log-ratio of the vote

shares of any two candidates j and j′ does not depend on the characteristics of

other candidates (this is the IIA property). An important implication is that,

if one candidate changes her policy, all other candidates gain or lose votes by

the same percentage. This makes little sense in a model of electoral politics,

19

as candidates on the same side of the ideology spectrum are naturally closer

substitutes than diametrically opposed candidates.

The key insight of BLP is that introducing voter heterogeneity allows flexible

substitution patterns to emerge. Voters with ideal points yi > 0, for instance,

are more likely to respond to a change in a right-wing candidate’s policy than

voters with yi < 0, which plausibly leads to higher substitutability between

right-wing candidates than between right versus left-wing candidates. This,

however, requires an alternative estimation procedure.

When voters are heterogeneous, candidates’ predicted vote shares integrate

over the probability P ijn(ν1i, ν2i) that voter i in state n selects candidate j

given her idiosyncratic policy preference shocks (ν1i, ν2i):

sjn =

∫ ∞−∞

∫ ∞−∞

P ijn(ν1i, ν2i)dΦ(ν1i)dΦ(ν2i)

=

∫ ∞−∞

∫ ∞−∞

exp(δjn +∑2

k=1 σkνkipkjn)

1 +∑

j′∈Jn exp(δj′n +∑2

k=1 σkνkipkj′n)

dΦ(ν1i)dΦ(ν2i), (4.6)

where Φ denotes the standard normal cumulative distribution function. Note

that predicted vote shares in state n, sn = (s1n, . . . , sJnn), now depend on

average utilities δn = (δ1n, . . . , δJnn) as well as the policy-preference variance

parameters σ = (σ1, σ2). BLP show that, though the transformation does not

have a closed-form solution as before, it is still possible to “invert” predicted

vote shares to recover voters’ average utilities. Specifically, given σ and ob-

served vote shares sn, there exists a unique vector of average utilities δn(σ) such

that predicted and observed vote shares match exactly, i.e., sn = sn(δn(σ), σ).

20

Then, using (4.3) and given θ = (α, γ, β, σ), we can compute the unobserved

candidate valence consistent with δjn(σ):

ξjn(θ) = δjn(σ)−2∑

k=1

(αk +D′nγk)pkjn −X ′jnβ. (4.7)

As in the homogeneous logit case, an IV moment condition identifies the pa-

rameters of the model. Provided we have valid instruments Zjn, i.e., a vector

of variables such that

E[Zjnξjn(θ)] = 0 if and only if θ = θ0, (4.8)

where θ0 denotes the true value of the model parameters, a Generalized Method

of Moments (GMM) estimator (Hansen 1982) can be constructed as follows.

Let Z and ξ(θ) denote the matrix and vector that vertically stack Z ′jn and

ξjn(θ) across candidates and elections in the data. Under standard technical

regularity conditions, the sample moment conditions 1J∗Z ′ξ(θ) converge to the

population moment conditions in (4.8) as J∗ →∞, where J∗ denotes the total

number of observations in the sample. Thus, given a positive-definite weighting

matrix WJ∗ , an asymptotically normal GMM estimator of θ0 is obtained by

minimizing the quadratic form

QJ∗(θ) = ξ(θ)′ZWJ∗Z′ξ(θ).

Inference follows standard GMM theory, including the choice of an optimal

21

weighting matrix.16

Computationally, the BLP estimation algorithm proceeds by iterating over

two nested loops. Given a candidate value of θ, the “inner loop” inverts pre-

dicted vote shares to solve for the average utilities δn(σ) consistent with the

data, which in turn are used to compute ξ(θ) according to (4.7). The “outer

loop” then searches over θ to minimize QJ∗(θ). This approach can be compu-

tationally inefficient, as the inner loop relies on costly fixed point calculations,

and very sensitive to convergence criteria. Instead, we implement an MPEC

version of the BLP estimator, which has been shown to yield better numerical

performance (Dube, Fox, and Su 2012). We describe our implementation and

provide additional technical details in Appendix B.

Instruments. As discussed, valid instruments are indispensable to identify

the parameters of the model. Importantly, a necessary condition for identi-

fication is that there must be at least as many variables in Zjn as there are

parameters to be estimated. Furthermore, in addition to satisfying the or-

thogonality restriction in (4.8), for precise inference a valid instrument should

be highly correlated with the variable whose coefficient it is identifying (this

is commonly known as instrument relevance). By assumption, candidates’ ob-

served valence characteristics are uncorrelated with unobserved valence and

are therefore valid (in fact, optimal) instruments to identify β. We rely on

auxiliary data and the structure of the model to obtain instruments for the

16We cluster standard errors at the district level, by electoral cycle, to allow for potentialcorrelation in unobserved valence across candidates in the same race.

22

remaining parameters.

To identify α and γ, notice that, given any variable that is correlated with pjn

but uncorrelated with ξjn, natural choices for the remaining instruments are its

square and corresponding interactions with state demographics. We consider

two types of instruments for pjn. First, we use the “BLP instruments,” i.e.,

the average observed valence characteristics of other candidates in the state.

These are uncorrelated with candidate j’s unobserved valence by assumption

but correlated with her policy choice in equilibrium given their influence on

voter preferences.

Second, we exploit the policy positions of (proximate) mayoral candidates in

the most recent local election in candidate j’s state. As shown in Figure

A.6, the policy positions of mayoral and federal legislative candidates serving

the same constituency covary. This is unsurprising since both types of can-

didates respond to similar electoral/party environments. However, mayoral

candidates’ policy positions are plausibly uncorrelated with the charisma or

other unobserved non-ideological attributes of federal legislative candidates.

Thus, we use a weighted average of same-party mayoral candidates’ positions

to instrument for pjn, giving a larger weight to mayoral candidates j′ closer to

j in terms of observed characteristics, i.e., with weights proportional to

exp−(Xjn −Xj′n)′Cov(X)−1(Xjn −Xj′n),

where Cov(X) denotes the covariance matrix of candidate characteristics in

the sample.

23

Finally, while the choice of instruments for (α, γ, β) follows standard intuition

from linear regressions given (4.7), the policy-preference variance parameters

(σ1, σ2) determine the nonlinear features of the model. Accordingly, we fol-

low common practice by employing nonlinear transformations (second-degree

polynomial) of the other instruments.

4.3 Voter Preferences: Estimates

In this section, we describe our first set of results. We begin by presenting our

estimates of the parameters in (4.1) and (4.2).

Tables A.4, A.5, and A.6 report, respectively, parameter estimates correspond-

ing to observable valence characteristics, party brands, and ideology. The first

column of each table presents estimates from a multinomial logit model that

does not account for voter demographics. This model rules out all ideological

heterogeneity among voters, with the only source of heterogeneity being re-

duced to the individual random utility shocks εijn, which are assumed to be

distributed TIEV. The second column presents estimates from a multinomial

logit model including voter demographics, which allows for ideological hetero-

geneity as a function of state-level covariates (in addition to εijn). The third

column presents estimates from the BLP model, which introduces ideological

heterogeneity among voters conditional on covariates. As a quick examination

of the tables reveals, the added complications of the BLP approach are worth

pursuing, as they have considerable bite in the resulting estimates.17

17Indeed, note that the three models are nested: the model in the second column isobtained by setting σ = 0, and the model in the first column additionally sets γ = 0. Table

24

Table A.4 displays the estimates of preferences for observed candidate char-

acteristics (βvalence). As suggested by Figure 1, these observable candidate

characteristics are important for voters. Voters prefer candidates that are

younger, more educated, and male. They also have a strong preference for

incumbents in both 2010 and 2014. On the other hand, voters tend to dislike

candidates with business experience or government bureaucrats.

Since the covariates are standardized, the coefficients can be compared at face

value. The gender preference is comparable in magnitude to the preference

against bureaucrats and slightly larger than the preference for candidates with

higher education. The largest effect, however, is associated with incumbency,

which is about four times as large as the gender preference.18 While broadly

consistent, these estimates exhibit notable differences across the three columns

of Table A.4, which highlights the importance of accounting for sources of

unobserved heterogeneity in voters’ preferences that could otherwise confound

the analysis.

Table A.5 displays estimates of the value of party brands (βbrands).19 If a

particular party brand is relevant for voters (carrying information or affect),

the corresponding coefficient should be different from zero. The results in-

A.6 shows that both restrictions are rejected by the data.18Potential sources of these incumbency effects include name recognition, accountability,

clientelistic networks, influence within parties, campaign resources, and other advantagesthat incumbents might enjoy. While other scholars have studied these in isolation (see, e.g.,Klasnja and Titiunik (2017)), we make no such attempt. Importantly, we allow incumbencystatus to bundle all persistent differences between incumbent and non-incumbent candidates,letting ξjn capture election-specific voter tastes for unobserved candidate characteristics.

19Electoral coalitions among parties in Brazil are very common and may even vary acrossdistricts within electoral cycle. We parsimoniously account for potential coalition effects byletting the “party brand” of coalition candidates be the sum of their own party’s and themean of other parties’ brands in the coalition.

25

dicate, however, that with a few exceptions (DEM, MDB) party brands are

generally not significant for voters’ decisions. This corroborates existing find-

ings in the literature on Brazilian politics that elections are fundamentally

candidate-centric rather than party-centric.

Finally, Table A.6 presents the estimates of voters’ ideological preferences

(α, γ, σ). The first-order question here is, do Brazilian voters care at all about

candidates’ policy positions? We find that they do. A voter at the average

value of demographic covariates and policy preference shocks υki has a mod-

erately left-wing ideal policy of −0.55 as well as decreasing utility for policies

further away from this bliss point. But voters’ ideal points vary significantly

with, and conditional on, their characteristics. Note, for instance, that an

increase in %rural makes voter i more left-wing whenever

∂2uij∂Drural

i ∂pjn= γrural1 + 2γrural2 pjn < 0.

Both γrural1 and γrural2 are statistically different from zero at conventional levels.

Moreover, at the point estimates, the condition above boils down to −17.426+

1.642pjn < 0, which is always satisfied since pjn ∈ [−5, 5] for all candidates in

the sample. Thus, voters in more rural districts tend to be more left-leaning

(see figure A.8 in the Appendix). Similarly, voters in districts that are older,

less educated, and with lower employment levels tend to be more left-wing

(although generally this depends on the policy level). Somewhat surprisingly,

voters in districts with a higher wage also tend to be left-leaning on average.

Interestingly, we find that voters’ policy preferences are heterogeneous even

26

conditional on demographic characteristics. While our point estimate of σ1

is essentially zero (and imprecisely estimated), our estimate of σ2 is positive

(2.42) and statistically significant. At face value, this uncovers substantial

within-district heterogeneity, which is magnified by the fact that it is the non-

linear rather than the linear effect of policy on voters’ preferences that exhibits

individual-level heterogeneity. In contrast with some of the existing literature,

this suggests ideological considerations are vibrant in Brazilian politics, and it

implies rich patterns of substitutability between candidates that inform their

(equilibrium) policy choices.

Evaluating our preference estimates at municipality-level covariates Dt, we

recover the average voter’s ideal point in each municipality.20 This is depicted

in Figure 4 (see also figure A.9 in the Appendix).

20Ideal points are constructed as follows. For each municipality, we simulate a sampleregistered voters, drawing for each voter i policy preference shocks (ν1i, ν2i) and randomutility shocks εijn. For voters with resulting concave policy preferences (α2i < 0), wecompute yi = −α1i/(2α2i). We then set p = max|q0.5(y)|, q99.5(y), where qr(y) denotesthe rth quantile of the yis. Finally, we truncate yi to lie in [−p, p], and, for voters withconvex policy preferences (fewer than 2.5%), we set yi = p (yi = −p) if α1i ≥ 0 (α1i < 0).

27

Figure 4: Voters’ Ideological Preferences by Municipality (in 2014): darker

blue (red) denotes more left-leaning (right) policy preference.

The estimates show a country broadly leaning left ideologically. This is consis-

tent with the political platform of the national executive in our sample, which

was held by Lula da Silva (PT) from 2003 to 2010, and by Dilma Rousseff

(PT) from 2011 to 2016. But the municipal estimates also show a substan-

tial amount of ideological heterogeneity across regions, and even within states.

The northeast and, in particular, south regions are more uniformly left-wing.

On the other hand, the southeast and central-west regions (Sao Paulo, Goias)

tend to be more conservative but highly polarized. A similar picture emerges

in the north, with states like Roraima leaning left and others like Tocatins

28

leaning right. Overall, this corroborates well-known patterns of partisanship

in Brazil.21

4.4 Welfare Gap

With our estimates at hand, we can evaluate voters’ welfare given the actual

set of candidates they face in the data, and compare this welfare with an ideal

(but attainable) benchmark.

To do this, we first use our preference estimates to compute expected voter

welfare (4.1) per municipality, given the set of candidates who participated in

the 2014 election. We approximate expected voter welfare in each municipality

by simulating a sample registered voters, drawing for each voter i policy pref-

erence shocks (ν1i, ν2i) and random utility shocks εijn. For each simulation, we

compute voter i’s welfare at her preferred candidate in the data given her re-

alized shocks. We then average over simulations to approximate the expected

welfare of each voter, and we finally average over voters in each municipality.

To compute the ideal benchmark, we average the utility voters would derive

from a hypothetical candidate with highest observed and unobserved in-sample

valence and policy at their ideal point. Using the realized and ideal measures

of welfare, we compute a “welfare gap” as the percentage distance between

the two measures. Figure 5 depicts the resulting welfare gap by municipality

for the 2014 election.

21See, for instance, the 2014 map in Power and Rodrigues-Silveira (2019).

29

Figure 5: Welfare Gap from “Ideal” Benchmark (2014 election): lighter shadeindicates observed welfare is closer to benchmark.

The results illustrate a considerable failure of the Brazilian political system.

The mean welfare loss with respect to the ideal benchmark across the 5,507

municipalities is 77%. Moreover, more than 90% of municipalities suffer a

welfare loss of at least 54%, while 25% of municipalities suffer a loss of at least

90% of the benchmark. Figure 6 plots the distribution of welfare losses across

municipalities by state. Interestingly, two of the richest states (Sao Paulo and

Rio de Janeiro), as well as the Distrito Federal and Mato Grosso do Sul, have

a median welfare loss above 87% of the benchmark. On the other hand, the

median welfare loss in Ceara, Amapa, and Rio Grande do Norte is below 70%.

While the education, experience, and other valence attributes of the pool of

candidates can be taken as fixed in the short-run, candidates can freely choose

30

Figure 6: Distribution of Welfare Losses across Municipalities by State (aspercentages of the benchmark).

their policy positions. An interesting question, then, is whether competitive

forces lead candidates to make policy concessions to voters. If this were the

case, the brunt of welfare losses would be due to deficiencies in valence char-

acteristics, not to ideological incongruence between voters and politicians.

In fact, we observe significant heterogeneity in this regard across states. Figure

7 plots the congruence between candidates’ policy positions and voters’ pol-

icy preferences in Rio de Janeiro and Maranhao for PMDB, PSDB, and PT

candidates. In Rio de Janeiro, the distribution of the policy positions of candi-

dates from all three major parties tracks the distribution of voter preferences

remarkably well. In Maranhao, however, the congruence between candidates

and voters is notably lower. To further illustrate this heterogeneity, Figure

31

A.10 in the Appendix plots the average pointwise distance between the distri-

bution of voters’ ideal points and the distribution of candidates’ positions for

the three major parties in all states.

PMDB (rj) PSDB (rj) PT (rj)

PMDB (ma) PSDB (ma) PT (ma)

Figure 7: Distribution of Candidates’ Policy Positions (bars) and Voters’ Pol-icy Preferences (line) in Rio de Janeiro and Maranhao for PMBD, PSDB, andPT Candidates.

To characterize how significant ideological incongruence is for welfare losses,

we decompose the welfare gap as follows. We compute an intermediate level

of welfare from a hypothetical election in which all candidates choose policies

as in the 2014 election, but they all have highest in-sample valence as in

the ideal benchmark. Thus, the percentage difference between welfare at the

ideal benchmark and this intermediate welfare value can be interpreted as the

fraction of the welfare gap due solely to ideological incongruence. Similarly,

32

the difference between the intermediate and realized welfare values can be

attributed solely to valence.

The left panel of Figure 8 plots the distribution of the municipality welfare

loss due to policy. In states like Santa Catarina, Rio Grande do Sul, Acre,

Tocatins, and Roraima, a considerable fraction of the welfare loss is brought

by a mismatch between voters’ ideological preferences and candidates’ policy

positions. Instead, in Rio de Janeiro, Ceara, Pernambuco, and Sao Paulo,

most of the welfare loss is due to shortages in candidates’ valence. Casual

inspection of this figure might suggest that the competitive pressures leading

to ideological congruence may be systematically different in rural and urban

states. The right panel of Figure 8 indicates that this is indeed the case. In

fact, rural states are much more likely to be poorly served in terms of ideology.

33

Figure 8: The left panel plots the distribution of the municipality welfare loss

due to policy in each state. The right panel plots the policy welfare loss and

valence welfare loss per municipality as a function of %rural.

In the following section, we delve into the “supply side” of politics to under-

stand why politicians make these choices.

5 Endogenous Policy Choice

The methodology for estimating voters’ preferences described in Section 4

recognizes that candidates’ policy positions are endogenous. The approach

relies on IVs to deal with this endogeneity. We now take preference estimates

as given, and turn to the task of estimating a model of the “supply side” of

politics, in which candidates’ positions emerge explicitly as equilibrium choices.

34

Understanding the considerations that lead candidates to diverge from voters’

preferences is particularly important in light of the substantial welfare losses

due to candidates’ policy choices uncovered in Section 4.

We model candidates’ policy positions as emerging from a balance – carried out

at the party level – between candidates’ own policy preferences and electability

of the party list. In a first-past-the-post electoral system, individual candidates

would fully internalize this tradeoff, contrasting the marginal benefit of an

increase in vote share with the marginal cost of a policy concession to voters.

In Brazil’s open-list PR system, however, individual policy choices can impose

externalities on other candidates, both from outside and within the party. The

party partially internalizes the externalities that each candidate imposes on

its own candidates, limited by each candidate’s strength within the party.22

We capture the strength of each candidate as the cost the party would face to

change policy away from the candidate’s ideal policy, and we allow this cost

to be a function of candidate-specific covariates, which we estimate. Having

estimates of both the “demand” and “supply” side of politics enables coun-

terfactual analyses of how the system would work under different conditions

from those observed in the data. We explore these in Sections 5.3 and 5.4.

22The degree of substitutability between candidates here is key and is thus part of themotivation for following the BLP estimation approach in Section 4.

35

5.1 Endogenous Policy Choice: Model and Estimation

There are L parties and N states. We think of the policy position of each

candidate j in party ` as emerging from a compromise between the goals of

the party and of the individual politician.23 The party wants to maximize its

share of seats in the legislature and would like to choose the policies of each

of its candidates accordingly. However, each politician finds it costly to adopt

a policy position that differs from her own ideal policy. We assume that the

party internalizes its politicians’ costs to varying degrees, depending on the

power of each politician within the party.

Denoting by J `n the set of candidates running for party ` in state n, by p`n

the vector of policy positions of all candidates in J `n, and by wn state n’s seat

share in the legislature, party `’s payoff is

Π` =N∑n=1

∑j∈J`

n

[wnsjn(p`n,p

−`n )− µ`jn|pjn − θjn|

]. (5.1)

Here, θjn denotes candidate j’s ideal policy, and we assume θjn ∼ N(θ`n, (σ`n)2),

where both the mean θ`n and standard deviation σ`n are functions of state

covariates. The parameter µ`jn reflects the weight that party ` puts on j’s

policy preferences and is given by

µ`jn = exp(A` +W ′

jnχ+ ζ`jn). (5.2)

23Our empirical results are unchanged if we conduct this analysis at the coalition (or list)level rather than the party level, which suggests the key tradeoffs occur within parties.

36

Here, A` is a party fixed effect, Wjn is a vector of observed characteristics of

the candidate and the state in which she runs, and ζ`jn is a candidate-specific

shock such that E[ζ`jn|Wjn] = 0, which is observed by the candidate and the

party but not by the analyst.24

Letting p` ≡ (p`1, . . . ,p`N) and p ≡ (p1, . . . ,pL), a (Nash) equilibrium is a

profile of policy choices p = (p1, . . . , pL) such that all parties are jointly best

responding, i.e., for all `,

p` ∈ arg maxp`

N∑n=1

∑j∈J`

n

[wnsjn(p`n, p

−`n )− µ`jn|pjn − θjn|

].

The equilibrium necessary first-order conditions for party ` in state n imply

the following for all of its candidates j ∈ J `n:

∂Π`(p)

∂pjn= 0 =⇒

∣∣∣∣∣wnpjnηjn,j sjn +

∑j′∈J`

n\j

ηj′n,j sj′n

∣∣∣∣∣ = µ`jn, (5.3)

where sj′n = sj′n(pn) and ηj′n,j =(∂sj′n(pn)

∂pjn

)(pjnsj′n

)is the elasticity in state

n of the vote share of candidate j′ with respect to the policy position of

candidate j. The parameter µ`jn captures the marginal cost for the party of

moving policy away from the candidate’s ideal point. In equilibrium, each

party sets policy so that this marginal cost equals the marginal benefit of

changing the candidate’s policy, which includes the effect of j’s policy change

on her own vote share, ηjn,j sjn, and its effect on the vote shares of other party

candidates,∑

j′∈J`n\j

ηj′n,j sj′n.

24In particular, Wjn includes j’s unobserved valence ξjn estimated in Section 4.

37

Taking logs and substituting expression (5.2), we can write (5.3) as

rjn ≡ log

∣∣∣∣∣wnpjnηjn,j sjn +

∑j′∈J`

n\j

ηj′n,j sj′n

∣∣∣∣∣ = A` +W ′

jnχ+ ζ`jn.

Note that all the components of rjn, including the equilibrium policy positions,

vote shares, and elasticities, are known from the data or from “demand-side”

estimates. We can then recover the coefficients A and χ by estimating the

linear model

rjn(j) = A`(j) +W ′jn(j)χ+ ζ

`(j)jn(j) for all j ∈ J∗, (5.4)

where n(j) and `(j) denote, respectively, the state and party for which j runs.

The key inputs that allow us to carry out this exercise and identify the supply-

side parameters are the flexible elasticity estimates that we obtained in Section

4 using the BLP approach.

5.2 Endogenous Policy Choice: Estimates

Tables 1 and A.7 present our estimates of the coefficients of the µ function

(5.2). For interpretation, note that a positive coefficient implies that a larger

value of the associated variable increases the party’s marginal cost of inducing

the candidate to adopt a policy position different from her preferred policy.

Recall from our voter preference estimates in Section 4.3 that incumbency,

education, youth, and lacking a business or bureaucratic background are va-

38

lence characteristics, which voters value. Notice that the coefficient estimates

associated with all these attributes are positive and statistically significant.

Hence, the first-order lesson from Table 1 is that being endowed with charac-

teristics that voters value empowers individual candidates, prompting parties

to choose policies that are more in line with the candidates’ own preferences,

to the detriment of party votes and voter welfare.25

“Supply Side” Estimates (µ function)

Age 0.036 Higher Education 0.313(0.028) (0.125)

Age Sq. -0.115 Business Exp. -0.168(0.023) (0.054)

Incumbent 2006 1.658 Gov. Experience -0.740(0.173) (0.098)

Incumbent 2010 2.295 Technician -0.057(0.145) (0.136)

Incumbent 2014 2.819 White Collar -0.095(0.200) (0.068)

Unobserved Valence 0.055 Gender -0.004(0.002) (0.197)

Table 1: Estimates of Coefficients χ (candidate characteristics) in Model (5.4).

In particular, incumbency has a large estimated effect, even when compared

with that of the candidate’s professional background or their education (all

dichotomous variables). This implies that parties face a significantly larger

cost of pushing incumbents to switch their policy positions away from their

ideal points relative to new candidates. On the other hand, gender is not

statistically significant.

Using these estimates, we can compute, for each party `, the (expected)

25This result is in the spirit of Aragones and Palfrey (2002), who show – in the context ofwinner-takes-all elections with two candidates – that candidates with a valence advantageadopt less moderate positions.

39

marginal cost of changing the policy position of each of its candidates, µ`jn. As

discussed, in equilibrium parties choose candidates’ policy positions so that

the marginal benefit of changing policy, the left-hand side of (5.3), equals this

marginal cost. Thus, the cost, together with vote-share elasticities in each state

– which reflect the intensity of electoral competition – determine candidates’

equilibrium policies.

Figure 9: Marginal Cost of Changes in Policy, and Policy Welfare Loss.

Figure 9 plots the vote-share-weighted average of µ`jn for each state, together

with the state average policy welfare loss from Section 4.4. The figure shows

that, on average, increases in the cost of adjusting policies lead to larger welfare

losses due to ideological incongruence between candidates and voters.

In the next section, we use the full equilibrium model of policy choice and voter

40

demand for candidates to further explore how changes in the characteristics

of the candidates running for office affect voter welfare.

5.3 Counterfactual: Better Candidates

A pressing concern for voters and scholars alike is the overall quality of demo-

cratic representation and whether institutional reforms aimed at recruiting

better candidates can improve voter welfare (Galasso and Nannicini 2011, Fer-

raz and Finan 2009). As we saw in the previous sections, however, candidates’

valence affects voter welfare both directly and indirectly, through its influence

on equilibrium policy choices. Because of this, reforms that may seem obvi-

ously beneficial to voters (such as increasing candidates’ education) might have

unintended consequences leading to lower, or even negative, welfare changes.

To evaluate this possibility, in this section we compute direct and indirect

changes in welfare resulting from an upward shift in the distribution of candi-

dates’ overall valence.26 Specifically, we consider a counterfactual scenario in

which candidates in the bottom three quartiles of the overall valence distribu-

tion draw a new valence value from the distribution of candidates in the top

quartile.27 To reduce the computational burden, we focus our analysis on the

state of Bahia, whose demographics are most representative of the nation as

26Overall valence is computed as the net sum of its observed and unobserved components,i.e., X ′jnβ + ξjn.

27In practice, when evaluating any particular policy change (gender quotas, minimal ed-ucation requirements, no reelection), we need to consider how it might affect other char-acteristics of the pool of candidates. While any such exercise is feasible in this context, itrequires taking a stance on such selection effects. Our proposed exercise allows us to bypassthese considerations, focusing instead on the effect of a pure valence improvement.

41

a whole.28

Figure 10 presents the results. The left panel plots welfare changes by munic-

ipality with fixed policy positions as in the data, while the right panel plots

welfare changes with equilibrium policies. Municipalities colored in lighter

purple (yellow) experience a higher welfare loss (gain). As we can see in the

left panel, keeping policies fixed at the old equilibrium, the valence shock has

an overwhelmingly positive effect on welfare. The direct effect of the valence

shock increases average voter welfare – measured as a percentage of ideal wel-

fare as in Section 4.4 – across municipalities by 20 percentage points with

respect to that in the data. Ninety percent of all municipalities attain an

increase in welfare of more than 9 percentage points, while the top quartile

registers an increase of average welfare of more than 28 percentage points.

When we consider the full equilibrium effect, however, the picture that emerges

is more nuanced. Average welfare still increases considerably, but now only

by 11.5 percentage points. Moreover, more than 10 percent of all municipal-

ities experience a welfare loss. This is also illustrated in Figure A.11 in the

Appendix, which shows the scatterplot by municipality of percentage changes

in welfare with respect to the data with fixed and equilibrium policies.

The analysis shows that the indirect equilibrium effects of changes in valence

can be both qualitatively and quantitatively significant, and should not be

glossed over when implementing reforms such as female quotas, minimal edu-

cation requirements, or reelection bans.

28We compute equilibrium policies in the counterfactual by best-response iteration start-ing from the policy positions observed in the data.

42

Fixed Policies Equilibrium

Figure 10: Welfare Change Following Counterfactual Valence Improvement, Bahia: lighterpurple (yellow) indicates higher welfare loss (gain). The left panel plots welfare changesby municipality with fixed policy positions. The right panel plots welfare changes withequilibrium policies.

5.4 Counterfactual: Party Consolidation

A striking feature of the Brazilian political system is the large number of

parties and candidates participating in elections, which has led scholars to

question the quality of governance in such a fragmented system (Figueiredo

and Limongi (2000)). Up to this point, we focused on how the characteristics

and number of electoral alternatives affect voter welfare. In this section, we

consider their effect on electoral outcomes. In particular, we examine the effect

of restricting political competition to the top eight parties.29

As in the previous counterfactual exercise, the constraint on the number of

29We also rule out coalitions in this counterfactual. See the discussion in Footnote 31.

43

parties fielding candidates for office has both a direct and an indirect effect.

A naive analysis would maintain the characteristics of the trimmed set of

candidates running for office fixed, and would simply compute how the votes

of the excluded candidates get distributed among the surviving candidates.

This, however, ignores equilibrium effects, i.e., that the “empty spaces” in the

ideological spectrum will prompt candidates to optimally relocate, leading to

further changes in vote shares. Thus, the full answer requires that we compute

a new equilibrium for the counterfactual set of candidates running for office.30

Figure 11 presents the main results of this exercise. With fixed policies, all

major parties gain representation in the chamber. The big winners here are

the DEM, going from 4% to 10% of the seats, the PMDB, going from 13%

to 20%, and PR, going from 7% to 14%. On the other hand, the PSDB, PT,

and SD parties see relatively small gains. When we consider full equilibrium

effects, however, results change considerably. The PMDB emerges as the clear

winner, obtaining 40% of the seats. PP and PR also register significant gains,

capturing 15% and 21% of the seats respectively. On the other hand, DEM,

PSD, and particularly the PT suffer considerable losses, even with respect to

the seat distribution observed in the data.31

This counterfactual experiment reaffirms not only the importance of indirect

30Once again, the flexibility of the BLP approach (in particular, dispensing with IIA)allows us to do this in a plausible way, without imposing overly restrictive or unrealisticsubstitution patterns on candidates’ policy choices.

31While a full analysis of the role of electoral coalitions is beyond the scope of this paper,it is notable that party consolidation effects seem to occur within coalitions. For instance,PMDB emerges as the clear standard-bearer of the “Com a Forca do Povo” coalition (seeTable A.2), capturing most of the seats lost by coalition partners PSD and PT. Similarly,DEM and SD seats transfer to PSDB, their larger partner in the “Muda Brasil” coalition.

44

Figure 11: Counterfactual: Party Consolidation. The figure plots seat sharesin the data (blue), in the immediate response to a trimming of competingparties without policy adjustment (orange), and with policies resulting froma new equilibrium (grey).

equilibrium effects, but also the richness of ideological competition in Brazil,

contrary to some views in the literature.32 Candidates’ strategic policy choices

have crucial consequences for voter welfare and election outcomes.

32Our findings align with more recent scholarship highlighting the growing relevance ofprogrammatic appeals in legislative elections (Hagopian, Gervasoni, and Moraes (2009)).

45

6 Conclusion

In this paper, we set out to evaluate how well the Brazilian political system

serves its voters. To that end, we estimate voters’ preferences over candidates,

viewing candidates as a collection of both pre-determined valence attributes

and endogenous policy positions. This allows us to quantify – for the first time,

to our knowledge – how much Brazilian voters value ideological representation

relative to valence, and how much weight voters give to individual candidate

characteristics relative to party labels.

Using these estimates, we evaluate voters’ welfare given the actual set of can-

didates they face in the data. We compare this welfare with an ideal (but

attainable) benchmark in which voters are well served in terms of both va-

lence and ideological representation. The results uncover a large failure of the

Brazilian political system that leads to an average welfare loss of 77% relative

to the benchmark across the 5,507 Brazilian municipalities.

We further examine the roots of this representation failure. Our estimates

imply that, in many states, a significant fraction of the welfare loss is due

to ideological incongruence between voters and politicians. To understand

why politicians make policy choices that diverge from the preferences of their

constituencies, we estimate a model of the “supply side” of politics, in which

candidates’ positions emerge explicitly as equilibrium choices. A key lesson

from this exercise is that candidates with valence advantages are able to put

forth policies that are more in line with their own preferences, to the detriment

of party votes and voter welfare. Relatedly, we also find that candidates’

46

power vis-a-vis the parties they represent explains a significant fraction of the

welfare loss to voters that is due to ideological incongruence. This complements

previous results in the literature on the consequences of weak parties in Brazil.

Through a series of counterfactual experiments, we explore the consequences

of potential institutional reforms aimed at improving the quality of represen-

tation and governance. By estimating a full model of candidate policy choice

and voter demand for candidate characteristics, we are able to gauge not only

the direct effects of such reforms, but also indirect effects through equilibrium

policy adjustments. Our results caution that what might at first glance seem

unambiguously beneficial to voters can have unintended equilibrium conse-

quences, which should not be glossed over when evaluating potential reforms.

We hope our analytical approach may provide guidance in this respect.

We also believe our approach can be fruitfully extended to other countries in

and outside the region. Doing so would allow us to better understand how well

different electoral institutions serve voters’ interests. Another fruitful direction

for future research is to integrate this approach with a model of selection into

politics. This would constitute, without a doubt, a considerable undertaking.

However, such an exercise would shed light on the long-term consequences of

electoral institutions. We hope that our first step in this direction encourages

others to explore these exciting research directions.

47

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50

A Appendix: Additional Tables and Figures

Representatives Population District Mag.

State Number % No. % Pop / Legs

Sao Paulo (sp) 70 13.6% 39,924,091 21.5% 570,344

Minas Gerais (mg) 53 10.3% 19,159,260 10.3% 361,495

Rio de Janeiro (rj) 46 9.0% 15,180,636 8.2% 330,014

Bahia (ba) 39 7.6% 13,633,969 7.3% 349,589

Rio Grande do Sul (rs) 31 6.0% 10,576,758 5.7% 341,186

Parana (pr) 30 5.8% 10,226,737 5.5% 340,891

Pernambuco (pe) 25 4.9% 8,541,250 4.6% 341,650

Ceara (ce) 22 4.3% 8,450,527 4.4% 371,822

Maranhao (ma) 18 3.5% 6,424,340 3.5% 356,908

Goias (go) 17 3.3% 5,849,105 3.1% 344,065

Para (pa) 17 3.3% 7,443,904 4.0% 437,877

Santa Catarina (sc) 16 3.1% 6,178,603 3.3% 386,163

Paraıba (pb) 12 2.3% 3,753,633 2.0% 312,803

Espırito Santo (es) 10 1.9% 3,392,775 1.8% 339,278

Piauı (pi) 10 1.9% 3,086,448 1.7% 308,645

Alagoas (al) 9 1.7% 3,093,994 1.7% 343,777

Amazonas (am) 8 1.6% 3,350,773 1.8% 418,847

Rio Grande do Norte (rn) 8 1.6% 3,121,451 1.7% 390,181

Mato Grosso (mt) 8 1.6% 2,954,625 1.6% 369,328

Distrito Federal (df) 8 1.6% 2,469,489 1.3% 308,686

Mato Grosso do Sul (ms) 8 1.6% 2,404,256 1.3% 300,532

Sergipe (se) 8 1.6% 2,036,227 1.1% 254,528

Rondonia (ro) 8 1.6% 1,535,625 0.8% 191,953

Tocantins (to) 8 1.6% 1,373,551 0.7% 171,694

Acre (ac) 8 1.6% 707,125 0.4% 88,391

Amapa (ap) 8 1.6% 648,553 0.3% 81,069

Roraima (rr) 8 1.6% 425,398 0.2% 53,175

Total 513 100.0% 185,712,713 100.0% 313,514

Table A.1: Number of Representatives per State, and District Magnitude.

51

states % rural

median wage literacy rate

Figure A.1: Socioeconomic Indicators, by Municipality.

52

Brazilian Chamber of Deputies Electoral Results 2014

Coalition Parties Votes % of votes Seats % of seatsWorkers'Party(PartidodosTrabalhadores,PT) 13,554,166 13.93% 68 13.26%BrazilianDemocraticMovementParty(PartidodoMovimentoDemocráticoBrasileiro,PMDB) 10,791,949 11.09% 66 12.87%ProgressiveParty(PartidoProgressista,PP) 6,429,791 6.61% 38 7.41%SocialDemocraticParty(PartidoSocialDemocrático,PSD) 5,967,953 6.13% 36 7.02%RepublicParty(PartidodaRepública,PR) 5,635,519 5.79% 34 6.63%BrazilianRepublicanParty(PartidoRepublicanoBrasileiro,PRB) 4,424,824 4.55% 21 4.09%DemocraticLabourParty(PartidoDemocráticoTrabalhista,PDT) 3,472,175 3.57% 19 3.70%RepublicanPartyoftheSocialOrder(PartidoRepublicanodaOrdemSocial,PROS) 1,977,117 2.03% 11 2.14%CommunistPartyofBrazil(PartidoComunistadoBrasil,PCdoB) 1,913,015 1.97% 10 1,95%Total 54,166,509 55,67% 303 59,07%

Brazilian Social Democracy Party (Partido da Social Democracia Brasileira, PSDB) 11,073,631 11.38% 54 10.53%Democrats(Democratas,DEM) 4,085,487 4.20% 21 4.09%BrazilianLabourParty(PartidoTrabalhistaBrasileiro,PTB) 3,914,193 4.02% 25 4.88%Solidarity(Solidariedade,SD) 2,689,701 2.76% 15 2.92%LabourPartyofBrazil(PartidoTrabalhistadoBrasil,PTdoB) 828,876 0.85% 2 0,39%NationalLaborParty(PartidoTrabalhistaNacional,PTN) 723,182 0.74% 4 0.78%NationalEcologicParty(PartidoEcológicoNacional,PEN) 667,983 0.69% 2 0.39%PartyofNationalMobilization(PartidodaMobilizaçãoNacional,PMN) 468,473 0.48% 3 0.58%ChristianLabourParty(PartidoTrabalhistaCristão,PTC) 338,117 0,35% 2 0.39%Total 24,789,643 25,47% 128 24,95%

BrazilianSocialistParty(PartidoSocialistaBrasileiro,PSB) 6,267,878 6.44% 34 6.63%PopularSocialistParty(PartidoPopularSocialista,PPS) 1,955,689 2.01% 10 1.95%HumanistPartyofSolidarity(PartidoHumanistadaSolidariedade,PHS) 943,068 0,97% 5 0.97%SocialLiberalParty(PartidoSocialLiberal,PSL) 808,710 0.83% 1 0.20%ProgressiveRepublicanParty(PartidoRepublicanoProgressista,PRP) 724,825 0.75% 3 0.58%FreeHomelandParty(PartidoPátriaLivre,PPL) 141,254 0.15% 0 0.00%Total 10,841,424 11,15% 53 10,33%

SocialChristianParty(PartidoSocialCristão,PSC) 2,520,421 2.59% 13 2.53%GreenParty(PartidoVerde,PV) 2,004,464 2.06% 8 1,56%SocialismandLibertyParty(PartidoSocialismoeLiberdade,PSOL) 1,745,470 1,79% 5 0.97%ChristianSocialDemocraticParty(PartidoSocialDemocrataCristão,PSDC) 509,936 0.52% 2 0.39%BrazilianLabourRenewalParty(PartidoRenovadorTrabalhistaBrasileiro,PRTB) 454,190 0.47% 1 0.20%UnitedSocialistWorkers'Party(PartidoSocialistadosTrabalhadoresUnificado,PSTU) 188,473 0.19% 0 0.00%BrazilianCommunistParty(PartidoComunistaBrasileiro,PCB) 66,979 0.07% 0 0.00%Workers'CauseParty(PartidodaCausaOperária,PCO) 12,969 0.01% 0 0,00%

Total valid votes 97,300,478 100,00% 513 100,00%

Pro-government Coalition "Com a Força do Povo"

Opposition Coalition "Muda Brasil"

Opposition Coalition "Unidos pelo Brasil"

Out of coalition (Fora de coligação)

Table A.2: Brazilian Chamber of Deputies Electoral Results 2014.

53

PT PMDB PSDB

Figure A.2: Party Vote Shares and Median Wage, by Municipality.

PT PMDB PSDB

Figure A.3: Party Vote Shares and High School Att., by Municipality.

54

Figure A.4: Effective Number of Parties (municipality-level vote shares) in the2014 Election, by State.

55

2006 2010 2014

State Full Sample Percent Full Sample Percent Full Sample Percent

Acre 50 34 68.00 37 29 78.38 62 50 80.65

Alagoas 82 55 67.07 63 40 63.49 99 64 64.65

Amazonas 78 41 52.56 51 31 60.78 76 46 60.53

Amapa 63 49 77.78 62 57 91.94 102 85 83.33

Bahia 216 134 62.04 243 145 59.67 287 186 64.81

Ceara 145 83 57.24 114 73 64.04 190 124 65.26

Distrito Federal 106 76 71.70 94 67 71.28 125 109 87.20

Espirito Santo 83 62 74.70 72 62 86.11 147 107 72.79

Goias 109 73 66.97 116 78 67.24 93 63 67.74

Maranhao 153 97 63.40 151 103 68.21 222 136 61.26

Minas Gerais 528 355 67.23 523 357 68.26 595 406 68.24

Mato Grosso Do Sul 70 53 75.71 67 46 68.66 114 80 70.18

Mato Grosso 92 64 69.57 68 42 61.76 86 66 76.74

Para 137 85 62.04 118 77 65.25 170 124 72.94

Paraiba 87 58 66.67 77 64 83.12 90 66 73.33

Pernambuco 198 98 49.49 176 90 51.14 152 100 65.79

Piaui 83 53 63.86 87 63 72.41 85 69 81.18

Parana 258 178 68.99 265 167 63.02 287 203 70.73

Rio De Janeiro 707 416 58.84 751 452 60.19 862 596 69.14

Rio Grande Do Norte 68 37 54.41 60 37 61.67 80 60 75.00

Rondonia 69 58 84.06 71 59 83.10 81 67 82.72

Roraima 81 56 69.14 61 48 78.69 77 71 92.21

Rio Grande Do Sul 279 206 73.84 271 184 67.90 305 236 77.38

Santa Catarina 131 108 82.44 147 109 74.15 124 80 64.52

Sergipe 48 33 68.75 54 39 72.22 72 58 80.56

Sao Paulo 952 671 70.48 1030 755 73.30 1239 871 70.30

Tocantins 70 49 70.00 40 34 85.00 46 39 84.78

Total 4943 3282 66.40 4869 3308 67.94 5868 4162 70.93

Table A.3: Proportion of Candidates with No Missing Data on Covariates (in

sample), by State and Electoral Cycle.

56

Figure A.5: Vote Share of Candidates With (1) and Without (0) Policy Data.

57

Figure A.6: Face Validity of Policy Measure.

Figure A.7: Progressive Movement to the Left of the Ideological Spectrum: in

our estimates (left) and in Latinborometer surveys (right).

58

MNL MNL (Covs) BLP (Covs)

Age -0.341 -0.065 -0.309

(0.123) (0.128) (0.093)

Age Sq. 0.091 0.032 0.102

(0.078) (0.060) (0.046)

Gender (male) 0.271 0.325 0.585

(0.267) (0.276) (0.221)

Incumbent 2006 1.316 1.222 0.829

(0.550) (0.648) (0.634)

Incumbent 2010 2.227 2.134 2.368

(0.611) (0.634) (0.519)

Incumbent 2014 2.018 2.108 2.470

(0.576) (0.699) (0.524)

Higher Education 0.216 0.513 0.410

(0.266) (0.217) (0.204)

Business Exp. -0.847 -0.500 -0.727

(0.270) (0.283) (0.215)

Government Exp. -0.733 -1.154 -0.527

(0.364) (0.338) (0.295)

Technician 0.282 0.568 0.464

(0.527) (0.582) (0.469)

White Collar 0.470 0.372 0.329

(0.396) (0.375) (0.267)

Table A.4: Parameter Estimates (βvalence): Observed Candidate Characteris-

tics.

59

MNL MNL (Covs) BLP (Covs)

DEM 0.472 1.404 2.429

(1.589) (1.361) (1.285)

PDT -0.552 -1.061 -0.157

(0.639) (0.458) (0.413)

MDB 0.576 -0.112 1.043

(0.787) (0.614) (0.505)

PP -1.583 -1.902 -0.651

(0.498) (0.552) (0.394)

PR 0.008 -0.185 0.070

(0.723) (0.507) (0.384)

PRB -1.098 -0.542 0.572

(0.823) (0.913) (0.814)

PSB -0.822 -1.511 -0.245

(0.613) (0.496) (0.455)

PSD 1.379 0.356 0.842

(1.136) (0.973) (1.050)

PSDB -1.324 -1.934 -0.911

(0.507) (0.502) (0.418)

PT -0.587 -1.209 0.425

(0.723) (0.547) (0.486)

PTB -0.315 -0.827 -0.084

(0.526) (0.555) (0.406)

Table A.5: Parameter Estimates: Party Brands (βbrands). We display only

estimates for parties with at least three million votes.

60

MNL MNL (Covs) BLP (Covs)

Policy (α1) 3.527 -4.869 -4.915

(1.416) (4.262) (3.886)

Policy × Median Wage (γwage1 ) -10.949 -7.556

(5.279) (4.613)

Policy × % Rural (γrural1 ) -22.329 -17.426

(7.569) (6.658)

Policy × % Higher Education (γedu1 ) 2.751 2.418

(3.301) (3.187)

Policy × % Employed (γemp1 ) 13.280 12.957

(7.451) (6.753)

Policy × Average Age (γage1 ) -6.273 -7.930

(3.629) (3.027)

Policy × % Female (γfemale1 ) -0.827 2.054

(4.611) (4.452)

Policy Sq. (α2) -1.968 -1.047 -4.461

(0.607) (0.445) (1.123)

Policy Sq. × Median Wage (γwage2 ) 0.316 -0.255

(0.568) (0.439)

Policy Sq. × % Rural (γrural2 ) 1.036 1.642

(0.642) (0.710)

Policy Sq. × % Higher Education (γedu2 ) 0.163 0.944

(0.330) (0.364)

Policy Sq. × % Employed (γemp2 ) 0.976 2.143

(0.693) (0.677)

Policy Sq. × Average Age (γage2 ) -0.779 -0.964

(0.310) (0.324)

Policy Sq. × % Female (γfemale2 ) 0.317 0.378

(0.447) (0.450)

Policy × Individual Ideology (σ1) 0.0002

(1127.6)

Policy Sq. × Individual Ideology (σ2) 2.423

(0.727)

Table A.6: Parameter Estimates: Policy Preference.

61

Figure A.8: Voters’ Policy Preferences (as a function of %rural in each mu-

nicipality).

Figure A.9: Distribution of Average Municipality Ideological Preference, by

State.

62

Figure A.10: Average point-by-point distance between distribution of voters’

ideal points and distribution of candidates’ positions for selected parties.

63

Figure A.11: Valence Improvement Counterfactual: % change in welfare with

fixed (horizontal axis) and equilibrium policies (vertical axis)

64

“Supply Side” Estimates (µ function)

State Characteristics

Median Wage -0.190 % Higher Education 0.435(0.290) (0.165)

% Rural 1.337 % Employed 4.546(0.359) (0.384)

Average Age -1.219 % Female 1.182(0.097) (0.228)

Party Fixed Effects

DEM -1.801 PDT -2.507(0.266) (0.318)

MDB -2.165 PP -2.173(0.352) (0.288)

PR -1.001 PRB -3.147(0.474) (0.538)

PSB -2.605 PSD -1.382(0.387) (0.452)

PSDB -2.176 PT -2.185(0.260) (0.287)

PTB -2.208(0.592)

Table A.7: Estimates of Coefficients χ (state characteristics) and Party FixedEffects A in Model (5.4).

65

B Appendix: Estimation of Voters’ Prefer-

ences

B.1 GMM Estimation and Inference

As discussed in Section 4.2, a GMM estimator of the parameters of our model

can be obtained by minimizing the quadratic form

QJ∗(θ) = ξ(θ)′ZWZ ′ξ(θ),

where ξjn(θ) is defined by (4.7). Under standard GMM regularity conditions

(see Hansen (1982) and Berry, Levinsohn, and Pakes (1995)), this estimator,

θ, satisfies

√J∗(θ − θ0)

d→ N(0, (G′WG)−1G′WΩW ′G(G′W ′G)−1)

as the sample size J∗ →∞. Here,

G = E[Zjn∇θξjn(θ0)] and Ω = E[Z ′jnξjn(θ0)ξjn(θ0)′Z ′jn]

are the gradient and variance, respectively, of the moment conditions (4.8).

Notice that the optimal weighting matrix W ∗ = Ω−1 minimizes the asymptotic

variance of the estimator, which then simplifies to (G′Ω−1G)−1. This suggests

a two-step estimation approach, which we follow.

In a first step, a consistent but inefficient estimate θ of θ0 can be obtained

66

by minimizing QJ∗(θ) using any positive-definite matrix W .33 Then, allowing

for potential correlation in unobserved valence across candidates in the same

race, the optimal weighting matrix can be consistently estimated as W ∗ =

Ω−1 =(Z ′Vξ(θ)

′Z)−1

, where (Vξ(θ))jj′ = ξj(θ)ξj′(θ) if j and j′ compete in the

same race and (Vξ(θ))jj′ = 0 otherwise. In a second step, reestimating the

model using W ∗ delivers a consistent and efficient estimate θ of θ0. For robust

inference, again allowing for potential correlation in unobserved valence across

candidates in the same race, a consistent estimate of the asymptotic variance

of θ can be obtained as (G′Ω−1G)−1, where G = Z ′∇θξ(θ) and Ω = Z ′Vξ(θ)Z.

B.2 MPEC Approach

As noted in Section 4.2, the traditional BLP “nested fixed point” (NFXP)

algorithm for computing θ can be inefficient and very sensitive to convergence

criteria. We rely instead on the MPEC approach of Su and Judd (2012).

The key idea is that, rather than “inverting” vote shares at each step of the

optimization search, which involves costly fixed point calculations, we can

simply impose sjn(δn, σ) = sjn as explicit constraints on the optimization

program. Since modern optimization algorithms only enforce constraints at

convergence, this can considerably reduce the computational burden.

Further computational gains can be obtained by exploiting sparsity. Specifi-

cally, we estimate θ by solving the following mathematical program with equi-

33We employ an approximation of Ω−1 using the residuals of the homogeneous version ofour model with σ = 0. Recall that estimation in this case boils down to a linear regressionvia two-stage least squares.

67

librium constraints:

minθ,ξ,ψ

ψ′Wψ subject to

ψ = Z ′ξ and (B.1)

sjn(δn, σ) = sjn for all j, n, where (B.2)

δjn =2∑

k=1

(αk +D′nγk)pkjn +X ′jnβ + ξjn. (B.3)

Dube, Fox, and Su (2012) show that this MPEC and the traditional BLP

NFXP algorithm yield theoretically identical estimates of θ0, but the MPEC

approach delivers superior numerical performance. While the computational

cost of estimation may seem to increase by treating ξ and the moment condi-

tions ψ as auxiliary variables – and thus expanding the size of the optimization

problem – note that (B.1) and (B.3) are linear constraints and (θ, ξ) no longer

enter the objective function directly. This, together with the sparsity that

results from ξjn having no effect on vote shares outside of j’s district and elec-

toral cycle, adds to the computational advantages over NFXP from avoiding

repeated fixed point calculations.

Realizing these gains, however, requires state-of-the-art optimization software,

capable of handling problems with thousands of variables and nonlinear con-

straints. We implement our MPEC estimator using the industry-leading Kni-

tro.34 We employ Knitro’s Interior-Point/Conjugate-Gradient algorithm, to

which we provide exact first derivatives of the objective and constraints.

34https://www.artelys.com/en/optimization-tools/knitro

68